Farm subsidies are essential despite their financial burden for the following reasons:
Support for Marginal Farmers: Subsidies provide financial aid to small and marginal farmers, enabling them to access fertilizers, seeds, and irrigation facilities.
Stabilizing Food Supply: They help ensure consistent agricultural production, leading to food security for the nation.
Reducing Rural Inequalities: Subsidies mitigate income disparities in rural areas by supporting resource-poor farmers.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).